Question

What is an equation of the line that passes through the points (-1, -6), (6,1)?

Answer 1

Answer:

y = x - 5

Step-by-step explanation:

Given:

The points are (-1, -6) and (6, 1)

To find:

the equation of line that pass through the points

To determine the equation of the line, it will be in the form:

`\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}`

The slope formula is given as:

`$$m\text{ = }(y_2-y_1)/(x_2-x_1)$$`
`\begin{gathered} x_1=-1,y_1=-6,x_2=6,y_2\text{ = 1} \\ m\text{ = }(1-(-6))/(6-(-1)) \\ m\text{ = }(1+6)/(6+1)=\text{ }(7)/(7) \\ m\text{ = 1} \end{gathered}`

To get the y-intercept, we will use any of the given points and the slope

`\begin{gathered} Using\text{ point \lparen6, 1\rparen: x = 6, y = 1} \\ y\text{ = mx + b} \\ 1\text{ = 1\lparen6\rparen + b} \\ 1\text{ = 6 + b} \\ 1-6\text{ = b} \\ b\text{ = -5} \end{gathered}`

Next substitute the slope and y-intercept

`\begin{gathered} y\text{ = 1\lparen x\rparen + \lparen-5\rparen} \\ \\ The\text{ equation od the line becomes:} \\ y\text{ = x - 5} \\ \end{gathered}`